# The domain of a cartesian function from parametric equations

x = 2cot t

y = (sin t)^2

t is greater than 0 but less than or equal to pi/2

The cartesian can be found using trig identities to be:

y = 8/ (4+ x^2)

What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x = 0, and as t tends to 0, x tends to infinity.

Am I correct?

Thank you.

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
Your title says "domain" but in the body of your message you say "range". Which is it?

If you are thinking of the "cartesian equation" as y a function of x, then the domain is the set of all possible x values which is the set of all vaues of cot(t) for t between 0 and pi/2 and the range is the set of all y values which is the set of all values of (sin t)^2 for t between 0 and pi/2.

Sorry for the confusion! I meant the domain! Would my answer therefore be correct?

Thanks

HallsofIvy
Science Advisor
Homework Helper
Yes.